Evaluating Stress Distribution Pattern in Periodontal Ligament of Maxillary Incisors during Intrusion Assessed by the Finite Element Method

Statement of the Problem The use of miniscrews has expedited the true maxillary incisor intrusion and has minimized untoward side effects such as labial tipping. Purpose The aim of this study was to assess the stress distribution in the periodontal ligament of maxillary incisors when addressed to different models of intrusion mechanics using miniscrews by employing finite element methods. The degree of relative and absolute intrusion of maxillary incisors in different conditions was also evaluated. Materials and Method Finite element model of maxillary central incisor to first premolar was generated by assembling images obtained from a three-dimensional model of maxillary dentition. Four different conditions of intrusion mechanics were simulated with different placement sites of miniscrews as well as different points of force application. In each model, 25-g force was applied to maxillary incisors via miniscrews. Results In all four models, increased stress values were identified in the apical region of lateral incisor. Proclination of maxillary incisors was also reported in all the four models. The minimum absolute intrusion was observed when the miniscrew was placed between the lateral incisor and canine and the force was applied at right angles to the archwire, which is very common in clinical practice. Conclusion From the results yield by this study, it seems that the apical region of lateral incisor is the most susceptible region to root resorption during anterior intrusion. When the minimum flaring of maxillary incisors is required in clinical situations, it is suggested to place the miniscrew halfway between the roots of lateral incisor and canine with the force applied to the archwire between central and lateral incisor. In order to achieve maximum absolute intrusion, it is advised to place miniscrew between the roots of central and lateral incisors with the force applied at a right angle to the archwire between these two teeth.


Introduction
Correction of deep overbite can be accomplished through different treatment strategies. Nonsurgical methods include either extrusion of posterior teeth or intrusion of anterior teeth or both. The decision depends on several factors such as incisor display, smile line and vertical dimension of the patient's face. [1][2][3] In patients with great interlabial gap and gummy smile, intrusion of maxillary incisor is the treatment of choice. [4] Conventional methods for incisor intrusion include 2×4 appliances such as utility arch, Burstone intrusion arch or reverse curved arches. [5][6][7][8][9][10][11] Some adverse side effects such as labial tipping of upper anterior teeth might result. Therefore, anterior teeth protrusion would be the actual result of the intrusion arch mechanics in lieu of true incisor intrusion. [3,11] The use of temporary anchorage devices (TADs) has facilitated different types of tooth movements. [12][13][14][15][16] Miniscrews offer several advantages such as immediate loading, easy insertion and removal process, and several placement sites along with minimal expenses for the patient. [17] Previous investigations have reported successful intrusion of maxillary anterior teeth using miniscrews when relatively light forces were used. [17][18][19] It has been shown that true maxillary incisor intrusion would be possible with the use of miniscrews [18][19] and untoward side effects such as labial tipping has been reduced to a minimum, unlike the situations that conventional intrusion mechanics are employed. [20] Nevertheless, the placement site of the miniscrew as well as the point of force application play a very important role in the displacement of the incisor segment and therefore must be selected carefully. [21] It has been well documented that the principal factor in the initiation of orthodontic tooth movement is the biologic changes that take place in the PDL. However, due to the complex structure of the periodontal tissue, proper assessment of stress profiles and the resultant changes in it after application of orthodontic forces is difficult. [22] In order to assess the biomechanical factors such as stress, strain and displacement in the teeth as well as the surrounding structures genuinely, finite element method (FEM) was introduced to the field of biomechanical studies. [23] This method is used to evaluate complex structures biomechanically by dividing them into smaller pieces namely element and then carefully analyzing the assembled elements to form a mathematical model of a certain structure. [24] The results of FEM analysis not only depends on the force magnitude, but also the deformation of the structures as well as their geometries. [25] Since this method has the ability of assessing different shapes with different properties, it seems to be a viable method in analyzing the changes in the periodontal ligament and the surrounding structures following tooth movement. [26] The distribution of stress on the central incisor root with different morphologies under different types of orthodontic tooth movements has been evaluated. [27] The aim of this study was to use FEM to assess the stress profiles in the periodontal ligament of maxillary incisors during orthodontic intrusion via miniscrews.
This can lead to a better understanding of the best site of placement of the miniscrews and the point of force application for the desired type of tooth movement.

Materials and Method
The central incisor, lateral incisor, canine and first premolar were extracted from a 3D computer model of the maxillary teeth on an ovoid arch (3-D studios.com™).
Since the model was in the format of DXF, the teeth were defined as surfaces and thus needed to be turned into solid bodies. This process was carried out via the Auto Cad software (version 2011), and the format was   Table 1. The periodontal membrane was supposed to have a uniform thickness (0.25 mm) with a linear behavior, [24] even though this did not truly reflect the complex behavior of PDL, but this method has been shown to be valid for orthodontic loading in FEM studies. [28][29] During the next step, cortical bone was added to the 3D model. The thickness of the cortical bone started from 1 mm at the crest of alveolar bone and increased to 2 mm toward the apical area of the roots of the teeth. [30] The three-dimensional models of 0.018"×0.   Table 2. [ 33] In the sagittal plane, the miniscrews were fabricated 1 mm external to the bone to represent the thickness of the gingiva. [32] In the first model, the miniscrew was placed halfway between the roots of central and lateral incisors and the force was applied at a right angle to the archwire between these two teeth.
In the second model, the miniscrew was placed halfway between the roots of lateral incisor and canine and the force was applied to a point on the archwire between the central and lateral incisors.
In the third model, the miniscrew was placed halfway between the roots of lateral incisor and canine and the force was applied at a right angle to the archwire between the lateral incisor and canine.
In the fourth model, the miniscrew was placed halfway between the roots of central and lateral incisors and the force was applied to a point on the archwire between lateral incisors and canine.
In each model, the finite element analysis was realized by applying a total of 25 g force from the miniscrew to the arch wire. [1] The total number of elements used in this finite element model was 67780 elements and 119583 nodes.
Boundary conditions were assigned to the nodes on the cortical bone above the apical area of the teeth as zero displacement in all directions. All the other nodes had 3 translational degree of freedom (X: mesiodistal; Y: vertical; Z: vestibulopalatinal).

Statistical analysis
Descriptive analysis was used to analyze the degree of displacement in the Y plane (vertical) as well as Z plane (vestibulopalatinal). Using the finite element analysis, the stress profiles in the periodontium of the central and lateral incisors were also defined.

Results
In all models, the highest stress magnitude was pro-   Table 11. In order to compare the values for absolute and relative intrusion in the four models in Table 11 more readily, the smallest value was considered as the base (100) and the rest of the values were ranked accordingly. The results are presented in Table 12.
In all four models of loading except for the first model, the labial displacement of the lateral incisor (Z plane) was more than the central incisor. The maximum   In all four models except for the first model, the When four different models of the study were compared, it was observed that in the first and second models, root divergence was reported between the central and lateral incisors; as the central incisor experienced an uncontrolled tipping movement of the crown to distal and labial along with intrusion; while, in the lateral incisor, an uncontrolled tipping of the crown was recorded to mesial and labial. On the other hand, in the third and fourth models, a convergence was experienced between the root of the incisors, as both the central and     was not statistically significant. [19] It should be considered that the center of resistance depends on several factors such as the surrounding bone, morphology and the length of the roots, and the inclination of the upper teeth. Therefore, the optimal point for the applied force depends on the individual variations. [37] In all four different models, Von Mises stress distribution was recorded to be the highest in the apex of the lateral incisor. This can be attributed to the smaller surface area and geometry of the apex of the lateral incisor. [39] This area should be considered as a point high ly prone to resorption in intrusive mechanics. This result was in consistence with previous histological findings that reported the concentration of the cell-free area and hyalinization zones at the apex which corresponded to   higher stress in that area. [40] It was also reported that a substantial amount of stress was created in the cementum and PDL as a whole. [41] Since the stress is the principal cause of the biomechanical response, it is expected the maximum absolute intrusion be recorded in the lateral incisor as well.
However, the maximum absolute intrusion was ob-

Conclusion
The apical region of lateral incisor experienced the highest stress levels. This site should be considered as the most susceptible site to resorption. The maximum absolute and relative intrusion was obtained in the first model. Therefore, in clinical situation in which intrusion